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Ratio Working Paper No. 345: Regularized Conditional Estimators of Unit Inefficiency in Stochastic Frontier Analysis, with Application to Electricity Distribution Market

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Electricity Distribution, Productivity, Regularized Posterior Likelihood, Stochastic Frontier Analysis
Ratio Working Paper No. 345
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Abstract

The practical value of Stochastic Frontier Analysis (SFA) is positively related to the level of accuracy at which it estimates unit-specific inefficiencies. Conventional SFA unit inefficiency estimation is based on the mean/mode of the inefficiency, conditioned on the estimated composite error. This approach shrinks the inefficiency towards its mean/mode, which generates a distribution that is different from the distribution of the unconditional inefficiency; thus, the accuracy of the estimated inefficiency is negatively correlated with the distance the inefficiency is located from its mean/mode. We propose a regularized estimator based on Bayesian risk (expected loss) that restricts the unit inefficiency to satisfy the underlying theoretical mean and variation assumptions. We analytically investigate some properties of the maximum a posteriori probability estimator under mild assumptions and derive a regularized conditional mode estimator for three different inefficiency densities commonly used in SFA applications. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimator outperforms the conventional (unregularized) approach when the inefficiency is greater than its mean/mode. With real data from electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators give substantially different results for highly inefficient companies.

Zeebari, Z., Månsson, K., Sjölander, P. & Söderberg, M. (2021). Regularized Conditional Estimators of Unit Inefficiency in Stochastic Frontier Analysis, with Application to Electricity Distribution Market. Ratio Working Paper No. 345. Stockholm: Ratio.

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Ratio Working Paper No. 345: Regularized Conditional Estimators of Unit Inefficiency in Stochastic Frontier Analysis, with Application to Electricity Distribution Market
Working paperPublication
Zeebari, Z., Månsson, K., Sjölander, P. & Söderberg, M.
Publication year

2021

Published in

Ratio Working Paper

Abstract

The practical value of Stochastic Frontier Analysis (SFA) is positively related to the level of accuracy at which it estimates unit-specific inefficiencies. Conventional SFA unit inefficiency estimation is based on the mean/mode of the inefficiency, conditioned on the estimated composite error. This approach shrinks the inefficiency towards its mean/mode, which generates a distribution that is different from the distribution of the unconditional inefficiency; thus, the accuracy of the estimated inefficiency is negatively correlated with the distance the inefficiency is located from its mean/mode. We propose a regularized estimator based on Bayesian risk (expected loss) that restricts the unit inefficiency to satisfy the underlying theoretical mean and variation assumptions. We analytically investigate some properties of the maximum a posteriori probability estimator under mild assumptions and derive a regularized conditional mode estimator for three different inefficiency densities commonly used in SFA applications. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimator outperforms the conventional (unregularized) approach when the inefficiency is greater than its mean/mode. With real data from electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators give substantially different results for highly inefficient companies.

Ratio Working Paper No. 345: Regularized Conditional Estimators of Unit Inefficiency in Stochastic Frontier Analysis, with Application to Electricity Distribution Market
Working paperPublication
Zeebari, Z., Månsson, K., Sjölander, P. & Söderberg, M.
Publication year

2021

Published in

Ratio Working Paper

Abstract

The practical value of Stochastic Frontier Analysis (SFA) is positively related to the level of accuracy at which it estimates unit-specific inefficiencies. Conventional SFA unit inefficiency estimation is based on the mean/mode of the inefficiency, conditioned on the estimated composite error. This approach shrinks the inefficiency towards its mean/mode, which generates a distribution that is different from the distribution of the unconditional inefficiency; thus, the accuracy of the estimated inefficiency is negatively correlated with the distance the inefficiency is located from its mean/mode. We propose a regularized estimator based on Bayesian risk (expected loss) that restricts the unit inefficiency to satisfy the underlying theoretical mean and variation assumptions. We analytically investigate some properties of the maximum a posteriori probability estimator under mild assumptions and derive a regularized conditional mode estimator for three different inefficiency densities commonly used in SFA applications. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimator outperforms the conventional (unregularized) approach when the inefficiency is greater than its mean/mode. With real data from electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators give substantially different results for highly inefficient companies.

Ratio Working Paper No. 349: Industrial conflict in essential services in a new era – Swedish rules in a comparative perspective
Working paperPublication
Karlson, N.
Publication year

2021

Published in

Ratio Working Paper

Abstract

This paper examines whether the Swedish regulatory system of dealing with industrial conflicts that affect essential services need an update or reform. Are the existing rules effective in a world where many essential services are upheld by many interdependent agents in complex systems where every single node becomes critical for the functioning of the system, and where the essential service activities could be either private or public? A comparative study is conducted with the corresponding regulatory systems of the United Kingdom, Germany, and Denmark.
The conclusion is that Sweden is a special case. The Swedish protection against and readiness in dealing with societally harmful industrial conflicts in essential services is weaker than in the countries of comparison. Just as in relation to other threats to essential services, it is not sustainable to claim that just because such a threat is not currently present, there would be no need for preparedness.
There are many alternative ways to handle this. Desirable methods should both prevent harmful conflicts from erupting and end conflicts that have grown harmful to society at a later stage. The labour market organisations should have a mutual interest in reforming the rules.

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